In a call centre, agents may handle calls at different speeds, and also may be more or less successful at resolving customers’ inquiries, even when only considering customers calling with similar requests. One common measure of successful call resolution is whether or not the call results in the customer calling back. This presents a natural trade-off between speed and quality, where quality is defined by the percentage of the agent’s calls that result in callbacks. The relevant control is the routing; that is, the decision concerning which agent should handle an arriving call when more than one agent is available.
In an inverted-V model setting, we formulate an optimization problem with the dual performance objective of minimizing customer wait time and minimizing the callback rate. We solve this optimization problem asymptotically, as the system size becomes large. This motivates a routing control for the discrete-event system, and we show via simulation that that routing control is on the efficient frontier. In particular, any routing control that has a lower average wait time (callback rate) must also have a higher callback rate (average wait time). The natural follow-on question is: what happens when the agents are strategic; that is, each agent may increase or decrease his service speed and service quality in response to performance incentives. In this current and on-going research, we propose one payment scheme and argue that it induces the agent service speed and quality that achieves minimum cost.